Predicate Logic and Integer Multiples Quiz
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Questions and Answers

What is the identity element of the group mentioned in the text?

  • Diagonal matrix
  • Symmetric matrix
  • n x n zero matrix (correct)
  • Identity matrix
  • What is the additive inverse of an element in the group?

  • Reciprocal element
  • Inverse element
  • Opposite element
  • Negative element (correct)
  • Which operation defines the group in the text?

  • Matrix multiplication
  • Matrix addition (correct)
  • Vector addition
  • Scalar multiplication
  • What type of numbers are represented by the general element z in the group C?

    <p>Complex numbers</p> Signup and view all the answers

    Which property shows that (C, +) forms an abelian group?

    <p>Commutative property</p> Signup and view all the answers

    What type of field is formed by (C, +, ·) according to the text?

    <p>Complex field</p> Signup and view all the answers

    What is the predicate isMultipleOfThree defined as?

    <p>A predicate that yields True if its input is an integer multiple of 3</p> Signup and view all the answers

    What does the set {x ∈ Z | isMultipleOfFive(x) ∧ ¬isMultipleOfThree(x) ∧ x > 0} represent?

    <p>Integers that are multiples of 5 but not multiples of 3</p> Signup and view all the answers

    What is the inverse of an element s in the group (R \ {0}, (a, b) → a · b)?

    <p>1 / s</p> Signup and view all the answers

    What operation forms the group (R \ {0}, (a, b) → a · b)?

    <p>Multiplication</p> Signup and view all the answers

    What does the matrix set G represent?

    <p>Set of non-singular n x n matrices with real entries</p> Signup and view all the answers

    In the context provided, which property must hold for a group operation to be considered associative?

    <p>Associativity</p> Signup and view all the answers

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